I don't ride there but I've driven it occasionally so I know it's busy and drivers are quite aggressive. Also, I'm not familiar with the "newish sidewalk/bike path thing," so this is pretty general but here goes.
Why not take the lane? There are three of them there, unless they've restriped to two. In either case, the right-most car lane feeds Williams so no problem being in it to keep on your route. With the bike lane full, it seems dangerous to me to stay in the middle of Weidler with traffic flying by, and I'd personally just as soon move onto Williams. I get that some in the bike lane might feel "shoaled" (shades of "fairweather floodgates
" thread on the front page) but heck, they can duck out of the bike lane and join you for a bit more mass
if they're all that critical